Can AI be used to reverse engineer a black box?
Yes this is entirely possible. As was previously mentioned, complex connectionist systems are often thought of as black boxes(despite us being able to "look in" the box given enough computation and analysis) because of the difficulty in understanding learning and the networks ultimate decision making.

Here, we can model the problem as such: given an input of filter settings(and presumably some information about the audio), predict the target descriptors as an output. All you really need to do is generate a dataset from the program and then train it in a multi-label classification context to predict the output descriptors.